e_atan2.c (3718B)
1/* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12/* __ieee754_atan2(y,x) 13 * Method : 14 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 15 * 2. Reduce x to positive by (if x and y are unexceptional): 16 * ARG (x+iy) = arctan(y/x) ... if x > 0, 17 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 18 * 19 * Special cases: 20 * 21 * ATAN2((anything), NaN ) is NaN; 22 * ATAN2(NAN , (anything) ) is NaN; 23 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 24 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 25 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 26 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 27 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 28 * ATAN2(+-INF,+INF ) is +-pi/4 ; 29 * ATAN2(+-INF,-INF ) is +-3pi/4; 30 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 31 * 32 * Constants: 33 * The hexadecimal values are the intended ones for the following 34 * constants. The decimal values may be used, provided that the 35 * compiler will convert from decimal to binary accurately enough 36 * to produce the hexadecimal values shown. 37 */ 38 39#include "math_libm.h" 40#include "math_private.h" 41 42static const double 43tiny = 1.0e-300, 44zero = 0.0, 45pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 46pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 47pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 48pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 49 50double attribute_hidden __ieee754_atan2(double y, double x) 51{ 52 double z; 53 int32_t k,m,hx,hy,ix,iy; 54 u_int32_t lx,ly; 55 56 EXTRACT_WORDS(hx,lx,x); 57 ix = hx&0x7fffffff; 58 EXTRACT_WORDS(hy,ly,y); 59 iy = hy&0x7fffffff; 60 if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)|| 61 ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */ 62 return x+y; 63 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 64 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 65 66 /* when y = 0 */ 67 if((iy|ly)==0) { 68 switch(m) { 69 case 0: 70 case 1: return y; /* atan(+-0,+anything)=+-0 */ 71 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 72 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 73 } 74 } 75 /* when x = 0 */ 76 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 77 78 /* when x is INF */ 79 if(ix==0x7ff00000) { 80 if(iy==0x7ff00000) { 81 switch(m) { 82 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 83 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 84 case 2: return 3.0*pi_o_4+tiny;/* atan(+INF,-INF) */ 85 case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */ 86 } 87 } else { 88 switch(m) { 89 case 0: return zero ; /* atan(+...,+INF) */ 90 case 1: return -zero ; /* atan(-...,+INF) */ 91 case 2: return pi+tiny ; /* atan(+...,-INF) */ 92 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 93 } 94 } 95 } 96 /* when y is INF */ 97 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 98 99 /* compute y/x */ 100 k = (iy-ix)>>20; 101 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 102 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 103 else z=atan(fabs(y/x)); /* safe to do y/x */ 104 switch (m) { 105 case 0: return z ; /* atan(+,+) */ 106 case 1: { 107 u_int32_t zh; 108 GET_HIGH_WORD(zh,z); 109 SET_HIGH_WORD(z,zh ^ 0x80000000); 110 } 111 return z ; /* atan(-,+) */ 112 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 113 default: /* case 3 */ 114 return (z-pi_lo)-pi;/* atan(-,-) */ 115 } 116}